Area versus Perimeter

Discussion in 'General Math' started by anheiserb, Nov 14, 2006.

  1. anheiserb

    anheiserb Guest

    Can someone please explain how to answer this question? Thanks....

    The perimeter of leaf II is 1.5 times as long as the perimeter of leaf
    I. How many times greater is the area of leaf II than the area of
    leaf I? Express your answer as a decimal to the nearest hundredth.

    Thanks again,
    Jeff
     
    anheiserb, Nov 14, 2006
    #1
    1. Advertisements

  2. anheiserb

    W H G Guest

    The unstated assumption is that the leaves are
    geometrically similar. That means that all
    lengths are multiplied by the same amount, in
    this case given as 1.5. Perimeter is a length so
    it is proportional to the length ratio; area depends
    on a length squared so it goes up as the length
    squared.
    Area leaf II / Area leaf I = Perim. of II/ Perim of I

    so area ratio = 1.5^2

    If you want to do it by baby steps, pretend the leaves
    are rectangles and put in some reasonable numbers.


    ----- W H G
     
    W H G, Nov 14, 2006
    #2
    1. Advertisements

  3. Whew, a clue.
    You are making gibberish. Don't you mean
    Area leaf II / Area leaf I = (Perim. of II/ Perim of I)^2 ?
     
    William Elliot, Nov 14, 2006
    #3
  4. anheiserb

    W H G Guest

    8-( right you are.
     
    W H G, Nov 14, 2006
    #4
  5. anheiserb

    John Bailey Guest

    Not to be a wa but the problem is incompletely specified. The edges
    of various leaves have different fractal dimensions.
    http://hypertextbook.com/facts/2002/leaves.shtml
    "The purpose of this lab is to determine the dimensions of six
    different leaves. The dimensions that were obtained ranged from 1.7 to
    1.9."
    Further, the scale at which the length is measured must be specified.
    If a scale of 1mm (for example) is used for both leaves I and II, then
    the answer given by other posts (1.5^2) must be increased (a smaller
    relative scale is implied in its perimeter measurement--thus a greater
    length will result.) I think the increased value would be 2.44 instead
    of 2.25 for a maple leaf (fractal dimension 1.9)

    I am sorry to confuse the issue. Fractal dimensions are a bit
    advanced for the original post's context, but hopefully, it will
    stimulate some further exploration of an interesting subject.

    http://tinyurl.com/yxxhvn
    Fractals in biological Science.
    "In fractal geometry, the fractal dimension is a statistical quantity
    that gives an indication of how completely a fractal appears to fill
    space, as one zooms down to finer and finer scales"

    John
     
    John Bailey, Nov 15, 2006
    #5
  6. anheiserb

    Roger Bagula Guest

    I found this yesterday:
    http://mathworld.wolfram.com/IsoperimetricQuotient.html
     
    Roger Bagula, Nov 16, 2006
    #6
    1. Advertisements

Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.